import matplotlib.pyplot as plt
import scipy as sp
sp.random.seed(12345)
n=1000 # n is the number of observations
n1=100 # we need to drop the first seveal observations
n2=n+n1 # sum of two numbers
alpha=(0.1,0.3) # GARCH (1,1) coefficients alpha0 and alpha1, see Equation (3)
beta=0.2
errors=sp.random.normal(0,1,n2)
t=sp.zeros(n2)
t[0]=sp.random.normal(0,sp.sqrt(a[0]/(1-a[1])),1)
for i in range(1,n2-1):
t[i]=errors[i]*sp.sqrt(alpha[0]+alpha[1]*errors[i-1]**2+beta*t[i-1]**2)
y=t[n1-1:-1] # drop the first n1 observations
#title('GARCH (1,1) process')
x=range(n)
plt.plot(x,y)
